Main interest of the present paper is to investigate the criticality of characteristic vector fields on almost cosymplectic manifolds. Killing critical characteristic vector fields are absolute minima. This paper contains some examples of non-Killing critical characteristic vector fields.

J. Eells and L. Lemaire, Selected topics in harmonic maps, CBMS Regional Conference Series in Mathematics, 50. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1983